I’m trying to change the cartridge on a Moen bathroom faucet but can’t get the handle off. The handle base will turn counter-clockwise but reaches a certain point and stops. You can also unscrew the part of the handle that sticks out and remove it but I don’t see a set screw to turn. I’m the original owner but I don’t have a model number or instruction manual.
I have that exact one. Yes, there is a little screw under the cap that is on the top. You will need something with a fine edge on it to begin prying that up, I use a box knife, then once it is up a little, you can get a flat screwdriver tip under the lip and finish getting it off. Loosen that screw and the HANDLE comes off, but you still have to unscrew another nut underneath, and that needs a socket wrench. If you don't have one, plumbing stores and home centers sometimes sell inexpensive tubular steel sockets specially designed for this (they are no good for working on your car, but they are OK for these). Here is a picture of a set that covers all of the possible sizes, it sells for around $8 in most places (assuming USA). You only need one size but it's hard to know WHICH size as they are all different from one another by 1/32nd of an inch increments.
Just make sure your water is off BEFORE loosening that nut!
Once you get there, these stems are usually "washerless" in that they have a little O-ring that slides along a brass plate and over time that O-ring wears down. Sometimes all you need do is TIGHTEN that nut to squeeze that O-ring down a little harder. Try that first. If it still drips, then remove the nut and back out the stem, you will see where the O-rings sit. Get and install replacements, they sell them in kits.